Abstract
To guarantee the normal functioning of quantum devices in different scenarios, appropriate benchmarking tool kits are quite significant. Inspired by the recent progress on quantum state verification, here we establish a general framework of verifying a target unitary gate. In both the non-adversarial and adversarial scenarios, we provide efficient methods to evaluate the performance of verification strategies for any qudit unitary gate. Furthermore, we figure out the optimal strategy and its realization with local operations. Specifically, for the commonly-used quantum gates like single qubit and qudit gates, multi-qubit Clifford gates, and multi-qubit Controlled-Z(X) gates, we provide efficient verification protocols. Besides, we discuss the application of gate verification for the detection of entanglement-preserving property of quantum channels and further quantify the robustness measure of them. We believe that the gate verification is a promising way to benchmark a large-scale quantum circuit as well as to test its property.
Highlights
To build a large-scale and stable quantum system, efficient and robust benchmarking tools are essential [1]
Some common benchmarking tool kits developed in this spirit and widely applied in experiments are quantum tomography based on compressed sensing [4,5], tensor-network-based quantum
Inspired by the quantum state verification studies [23,24,25], we propose a general framework of the quantum gate verification based on the prepare-and-measure strategies, where the verifier prepares local pure states, acts the target gates on them, and performs projective measurements to verify the gates
Summary
The set of linear operations on A is denoted as L(HA) and the set of quantum states as D(HA). That is, the output state of the map IA→A ⊗ EA→B with the maximally entangled state as the input state. Note that as the channel E being an unitary U , the Choi state is a maximally entangled (pure) state, and we denote the unitary channel as U (·) = U · U †. The Choi state encodes all the information of the corresponding quantum channel, and one can obtain the output of the channel by the following relation:. The state-channel duality is essential to our work, which indicates that verifying the quantum channel is equivalent to verifying the Choi state. II that many results in the state verification can be applied to the current study
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